First of all, let's look at 2 Corinthians 6:14-15:
"Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship have light with darkness?  What does a believer have in common with an unbeliever?"Now, the first part of verse 14 is often quoted when speaking about/to a couple, where one partner is a believer while the other isn't. However, we have discovered that (or rather, tried to understand the context of which Paul is saying this in) 'unequally yoked' does not only necessarily mean marriage. It can also mean partnerships, friendships, companionship, etc. But you may argue, 'Didn't Jesus call us to spread the gospel to the unbelievers?' Yes, he did. Verse 14 speaks about the two extremes of belief (or lack thereof): righteous, wicked; light, darkness; believer, unbeliever.
Ipsomniac explained (paraphrased) it as: "Would you be friends with someone who hates your parents? Let alone want to get together with them and marry them?"
Would you be friends or get together with someone who was evil/bad, or someone who hated/disliked/disagreed with the heavenly being you worship? Would you be partners with someone who would constantly disagree with whatever you say/think/do?
Let's continue on with verses 16 to 17:
" What agreement is there between the temple of God and idols? For we are the temple of the living God. As God said: 'I will live with them and walk with them, and I will be their God, and they will be my people.'  Therefore, 'come out from them and be separate,' says the Lord. 'Touch no unclean thing, and I will receive you.'"Here, Paul is specifically talking about idols and idolatry. (under the obvious subheading in bold in the NIV: 'Warning against Idolatry') Of course, logically, this would also mean that a believer is not to be married to a non-believer, too. Is this a commandment? Personally, I'm not sure. Some say yes, some argue no. Is it, then, an advice? Perhaps. Bear in mind that I am but a curious person wanting to understand more about this so that I am able to explain it better, so please withhold any spiteful comments about the way I am interpreting this.
What I do believe, is that this is stated so we wouldn't get hurt. Imagine being with someone who does not share the same ideas, goals, and beliefs as you do. Wouldn't that be conflicting? Wouldn't that just hurt you and the other person in the end? Also since people tend to mimic those around them, wouldn't it make sense that being with people who are 'evil' and 'idolatrous' would lead you down that path too? You could argue that the opposite may happen as well, but let's be honest, we're more inclined to follow the ways of the world than the ways of God, because we're sinful by nature and human.
Okay, before jumping for the nearest weapon to swing at me for my comment, understand that I, too, have many friends and family that would be considered 'idolatrous' by Paul's standards, but I do not see them as 'intentionally evil', so it's up to your discernment. The main point Paul is trying to make (in my humble opinion), is to stay away from people who would intentionally lead you astray from your walk with God and cause you to sin.
Anyway, so does this mean we cannot marry a non-believer? Let's look at 1 Corinthians 7:12-16
"To the rest, I say this (I [Paul] not the Lord): If any brother has a wife who is not a believer and she is willing to live with him, he must not divorce her.  And if a woman has a husband who is not a believer and he is willing to live with her, she must not divorce him.  For the unbelieving husband has been sanctified through his wife, and the unbelieving wife has been sanctified through her believing husband. Otherwise your children would be unclean, but as it is, they are holy.  But if the unbeliever leaves, let is be so. The brother or sister is not bound in such circumstances; God has called us to live in peace.  How do you know, wife whether you will save your husband? Or how do you know, husband, whether you will save your wife?"
Okay, that's a pretty chunky text. It looks less intimidating in my bible lol. It's a bit contradicting as it reaches the end, in my opinion. So if a child(ren) born from the union of a believer and unbeliever is considered unholy if the believer divorces the unbeliever, then wouldn't the leaving of the unbeliever make the child unholy too? I have no idea how this works. I mean, I think I can kind of get it that the responsibility lies with the believer of the couple, but my stating that could potentially open a can of worms.
Anyway this passage (and the verses before this) talks about the reasons for whether divorce is applicable in certain circumstances, and about marriage with an unbeliever. So my argument here is: marriage with a non-believer can happen, and no I don't think God would condemn you for it, and neither should the world and the church community. Although, the couple would have to face the consequences of the marriage. Let's face it, God lets certain things happen for a reason, and He makes the good out of them. Maybe you got a calling or some sort of conviction to go out with this person, even marry them. I don't think you should feel guilty about it. Who knows, perhaps God is using you to impact someone's life.
At the same time, dating is not a ground for missionary work. Don't date just so you can convert the other person, or with the intention of changing them. Their conversion should be his/her choice, based on their own conviction, not because of wanting to impress you, or being forced to. Freewill, remember? (Also a heavily debatable topic, but our mediocre sense of logic can't wrap around how God works anyway) Furthermore, God has called us to be at peace. If there is no peace in your heart, pray about it. Discuss about it with your fellow believers. Talk about it with your non-believer partner/friend/companion, and then plan your next course of action.
A partner should be someone who is willing to protect you, respect you, trust you and nurture you into a better person, and vice versa. And if you fall, God will always be there to catch you, in any way, whether it's a way you like, or not.
Finally, this is just my two cents, my opinion and my interpretation. I am not some holy believer who has absolute knowledge and understanding of the Bible and how this whole Christianity-thing works. There are still many things in the book that I'm trying to understand and come to terms with. We're all still learning anyways.
1 A group where believers come together and discuss and share about the bible and its word↩
2 Yoke here means to carry a burden, not an egg (which was what I thought as a child right though teenage)↩